The title and some of the comments assume it would be something like if you take 15 extra minutes you would just die . When in reality it would just be an increase in cancer risk. If it were THAT contaminated they'd use the AREA CLOSED the article mentions anyways. To be fatal within days you need about 10,000 mSv of exposure. Even with heavy fallout, exposure would probably be around 10 mSv per hour.
I'd imagine the concern is the radioactive dust / fallout getting stuck onto the vehicle, clothes, and hair which would increase your exposure time; getting through that zone as quick as possible could limit that dust sticking. But that's just my guess.
If I saw that sign I'd be a hell of a lot more concerned than "oh, miniscule cancer risk later in life, meh, I guess I'll just slowboat this one".